{"paper":{"title":"Cyclicity in the harmonic Dirichlet space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.CV","authors_text":"Evgueni Abakumov (LAMA), Karim Kellay (IMB), Omar El-Fallah, Thomas Ransford","submitted_at":"2016-01-25T12:12:20Z","abstract_excerpt":"The harmonic Dirichlet space  $\\cal{D} (\\mathbb{T})$ is the Hilbert space of functions $f \\in L^2(\\mathbb{T})$ such that $$\\|f\\|_{\\cal{D} (\\mathbb{T})}^2 := \\sum_{n\\in\\mathbb{Z}} (1+|n|)|\\hat{f}(n)|^2 < \\infty.$$  We give sufficient conditions for $f$  to be cyclic in $\\cal{D} (\\mathbb{T})$, in other words, for $\\{\\zeta ^nf(\\zeta):\\ n\\geq 0\\}$  to span a dense subspace of $\\cal{D} (\\mathbb{T})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06572","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}